CN109060292B - Consider the wind shake implementation method of double coupled systems of radio frequency plasma CVD test - Google Patents
Consider the wind shake implementation method of double coupled systems of radio frequency plasma CVD test Download PDFInfo
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Abstract
The invention discloses a kind of wind shake implementation methods of double coupled systems of consideration radio frequency plasma CVD test, the second-order blind identification technology that it is primarily based on complex modal theory realizes the decoupling to coupling measurement signal, reliable parameter identification is carried out to separation signal using Bayes's spectrum density method based on full aerodynamic simulation again, separation/hybrid matrix, intrinsic frequency and the damping ratio of BMS have been obtained accordingly, to realize the amendment to the pneumatic force signal that distorts；For the coupled problem of architecture prototyping system, the present invention is on the basis of power is calibrated, the wind scorpion and equivalent static wind load calculation method for considering that super-high building structure three-dimensional coupling effect influences are established using harmonic excitation method, supplement and perfect HFFB itself are existing insufficient to a certain extent, keep acquired results more true, accurate.
Description
Technical field
The present invention relates to experimental technique improvement areas, in particular to a kind of double couplings for considering radio frequency plasma CVD test
The wind shake implementation method of system.
Background technique
Radio frequency plasma CVD (HFFB) technology is to assess one of the technical way of super high-rise building wind scorpion.Mostly
Number super high-rise building has the characteristics that preceding two ranks sidesway modal frequency is very close, may generate under wind action significant
Modal coupling effect (MCE).For carrying out the balance model system (BMS) of wind-tunnel HFFB test, it is abnormal that MCE can increase aerodynamic force
The modified difficulty of varying signal；And the wind induced structural vibration of prototype is analyzed, do not consider that the influence of MCE may significantly affect structure wind
The calculated result of vibration response and charming appearance and behaviour load.
Mainly have for the existing processing method in aerodynamic force amendment field: 1. not considering that the single mode of modal coupling effect is repaired
Just；2. ignoring the fixation mode shape correction of the interaction effect (WSI) of wind and structure；3. being estimated roughly according to aerodynamic characteristics
The straight line approximation method of meter.Also there is patent of invention to propose the signal correction method based on coupled signal separation, but the party in the recent period
Method assumes aerodynamic force under the log-log coordinate near intrinsic frequency in skew lines in signal identification.This hypothesis is de- in whirlpool
Establishment when falling frequency far from BMS intrinsic frequency, and no longer meet when vortex shedding frequency is close or equal to BMS intrinsic frequency oblique
Straight line assumes.Thus there may be certain errors for the modal parameter and true value of method identification.
Another problem is when carrying out wind induced structural vibration analysis according to HFFB test data, since there are modal couplings to ask
Topic, traditional quadratic sum evolution (SRSS) method have ignored the correlation between mode, can underestimate the dynamic response of practical structures, because
This must be using complete quadratic combination (CQC) method for considering modal coupling effect.It is relatively early that CQC method is used for structural analysis
It is under single direction ground seismic wave function, according to the specific features that earthquake is composed, using mode correlation coefficient come the mould of description scheme
State coupling effect.When early stage hardware advances are not horizontal good enough, this simplification has certain positive effect, and for Super High
The aseismic analysis of building still has in precision centainly to be guaranteed, but since it uses approximate it is assumed that being not stricti jurise
On CQC method, can only be referred to as seismic analysis of structures simplification CQC (SCQC) method.Wind induced structural vibration is analyzed, though
The wind vibration response of structure may be so underestimated using SRSS method, but then may be significant by the SCQC wind shake analysis for being used for structure
Over-evaluate the wind vibration response of structure, this is because SCQC is the derivation result based on the excitation of single seismic wave, model is substantially
A single-input multiple output, but between each rank mode generalized force be in this case it is stringent relevant, all with the ground of input
Seismic wave is directly related, thus just produces analysis of Earthquake Response Spectrum method.The wind load of structure will be more than earthquake load complexity, i.e.,
Be for being analyzed using the three-dimensional structure wind shake of HFFB technology, generalized force depend on two of structure basis pneumatically topple it is curved
Square and torque, the power of the correlation between this three depend on the interference effect of architectural appearance, wind speed and direction and neighboring buildings,
It there is no fear of the situation for occurring perfectly correlated between them, may result in using SCQC and provide relatively conservative result.
Summary of the invention
The purpose of the present invention is to overcome the shortcomings of the existing technology and deficiency, provides a kind of consideration radio frequency plasma CVD examination
The wind shake implementation method for the double coupled systems tested.
The purpose of the present invention is realized by the following technical solution: a kind of double couplings considering radio frequency plasma CVD test
The wind shake implementation method of system, so-called double coupled systems refer to that testing progress super-high building structure wind scorpion using HFFB grinds
When studying carefully, it is possible that balance model system and architecture prototyping system mode coupled problem.
Buffeting resonance for the modal coupling of BMS influences, the power calibration with universality that the invention proposes one, it
It is primarily based on decoupling of second-order blind identification (SOBI) the technology realization of complex modal theory to coupling measurement signal, then using based on complete
Bayes's spectrum density method of aerodynamic simulation carries out reliable parameter identification to separation signal, has obtained BMS test letter accordingly
Number separation/hybrid matrix, intrinsic frequency and damping ratio, to realize to amendment (the power school of the pneumatic force signal of distortion measurement
It is quasi-).
For the coupled problem of architecture prototyping system, the present invention uses harmonic excitation method on the basis of power is calibrated
(HEM) wind scorpion and equivalent static wind load calculating side for considering that super-high building structure three-dimensional coupling effect influences are established
Method, supplement and perfect HFFB itself are existing insufficient to a certain extent, keep acquired results more true, accurate.
Compared with the prior art, the invention has the following advantages and beneficial effects:
(1) Bayes's spectrum density method based on full aerodynamic simulation can effectively simulate aerodynamic force, on this basis
The modal parameter arrived is more accurate, especially for across resonance region.Simultaneously this method can to recognition result it is uncertain into
Row assessment.
(2) present invention considers three-dimensional coupling effect in wind shake analysis, makes resulting substrate moment of flexure response and equivalent static
Power wind load is more accurate.
Detailed description of the invention
Fig. 1 is the double coupled system work flow diagrams of embodiment.
Fig. 2 is the Bayes's spectrum density method flow diagram for considering aerodynamic characteristics.
Fig. 3 is aerodynamic force formula fitting figure, and the Bayes's spectrum density for considering aerodynamic characteristics is demonstrated by specific example
The reliability of postulation formula in method；Fig. 3 (a) down wind；Fig. 3 (b) beam wind to.
Fig. 4 is correction effect figure under modal coordinate, and Fig. 4 (a) first step mode responds q1；Fig. 4 (b) second-order modal response
q2；Wherein, the Chinese meaning of abscissa f/Hz are as follows: f indicates frequency；Hz indicates hertz, is the unit of frequency.Ordinate
Chinese meaning are as follows: first step mode respond q1Power spectral density；OrdinateChinese meaning are as follows: second-order mode
Respond q2Power spectral density.As seen from the figure, separation signal is only single peak, shows that this method has carried out effectively coupled signal
Decoupling；Pass through the comparison before and after signal correction after separation, it can be seen that the correction effect to separation signal is more satisfactory.
Fig. 5 is correction effect figure under physical coordinates；The pneumatic overturning moment Mx of Fig. 5 (a) balance model system；The day Fig. 5 (b)
The pneumatic overturning moment My of flat model system；The torque Mz that pneumatically topples of Fig. 5 (c) balance model system；Wherein: abscissa f/Hz
Chinese meaning are as follows: f indicate frequency；Hz indicates hertz, is the unit of frequency.Ordinate S (f) indicates power spectral density, different
Subscript indicates the power spectral density of corresponding different variables；SMx(f) power spectral density of pneumatic overturning moment Mx, S are indicatedMy(f) table
Show the power spectral density of pneumatic overturning moment My, SMz(f) power spectral density of the pneumatic torque Mz that topples is indicated.As seen from the figure, it surveys
Amount signal be coupled signal, and correct after signal by it is bimodal or it is unimodal effectively remove, show to have carried out effective amendment to signal.
Influence whether Fig. 6 is amendment to equivalent foundation load；The equivalent basic moment M x of Fig. 6 (a) architecture prototyping system；
The equivalent basic moment M y of Fig. 6 (b) architecture prototyping system；The equivalent base torque Mz of Fig. 6 (c) architecture prototyping system.
Influence whether Fig. 7 is modal coupling to equivalent foundation load；The equivalent basis of Fig. 7 (a) architecture prototyping system is curved
Square Mx；The equivalent basic moment M y of Fig. 7 (b) architecture prototyping system；The equivalent basic moment M z of Fig. 7 (c) architecture prototyping system.
Specific embodiment
Present invention will now be described in further detail with reference to the embodiments and the accompanying drawings, but embodiments of the present invention are unlimited
In this.
Embodiment 1
A kind of double coupled systems and its wind shake implementation method for high frequency base balance test, such as Fig. 1, double coupled systemes
System includes two coupled systems of balance model system and architecture prototyping system, and the wind shake implementation method of the dual system includes following step
It is rapid:
Step 1: voltage signal is obtained by wind tunnel test measurement；
Step 2: obtaining initial substrate load signal through static calibration；
Step 3: being calibrated by power, obtain final substrate load signal；
Step 4: signal after calibration being exported, acquisition signal is obtained；
Step 5: by acquisition signal reduced scale transformation, obtaining the foundation load of prototype；
Step 6: mode distribution coefficient matrix is acquired by modal analysis result；
Step 7: in conjunction with mode distribution coefficient matrix, obtaining substrate aerodynamic force；
Step 8: obtaining substrate moment of flexure and torque responsive；
Step 9: obtaining equivalent static wind load.
Further, initial substrate load signal is obtained through static calibration in step 2；Static calibration is usually advanced in factory
It is capable, for determining the transition matrix between analog signal that each component is exported with phase inductive sensing, eventually by transition matrix reality
Existing static(al) decoupling；
Further, the detailed process for calibrating to obtain final substrate load signal by power of step 3 is:
S3-1: plural numberization processing is carried out to measuring signal x (t), obtains complex signal
S3-2: to complex signalIt carries out albefaction and obtains signal after albefaction
S3-3: seeking orthogonal matrix V, so thatAnd then the complex signal after being separated
S3-4: under modal coordinate, intrinsic frequency is carried out to separation signal and damping ratios identify；
S3-5: the parameter obtained according to identification is modified separation signal；
S3-6: by revised separation signal backstepping, revised pneumatic load is obtained.
If x (t)=[Mx(t)My(t)Mz(t)]TFor the HFFB pneumatic overturning moment in model basis observed and torque structure
At vector signal, can be considered by one group of independent source signal qm(t) it mixes:
X (t)=Φmqm(t) (1)
Φ in formulamFor hybrid matrix, the vibration shape matrix being equivalent in dynamic structural analysis often assumes that its sequency spectrum can
It is inverse；qmIt (t) is then the principal coordinate function of balance model system.Following method can be used to x (t) to the isolated source signal of progress
qm(t):
To adapt to BMS, there are possible non-proportional damping situations, first carry out plural number to x (t) using Hilbert transform method
Change processing, on this basis to complex signalCovariance matrix:
Carry out Eigenvalues Decomposition, obtain corresponding eigenvectors matrix E and diagonal matrix characteristic value D, and thus obtain it is so-called
Whitening matrix W are as follows:
W=ED-1/2 (3)
By whitening matrix W to complex signalPrincipal component decomposition is carried out, signal after albefaction is obtained:
MeetFor unit battle array.It is similar with formula (1), complex signalIt can be expressed as
Above formula substitution formula (4) is obtained:
Wherein,
Its corresponding time delay correlation function matrix are as follows:
Due toIn each element it is mutually indepedent, and set its variance as 1；And signal after albefactionMiddle each element is orthogonal
Normalizing, therefore V must be orthogonal normalizing battle array.About the solution of orthogonal matrix V, JAD (Joint Approximate can be used
Diagonalization) method.The control condition of this method is marked using non-diagonal element quadratic sum minimum as measurement
It is quasi-.After obtaining orthogonal matrix V, following hybrid matrix and separation matrix can be obtained:
Source (principal coordinate) signal of the isolated decoupling to signal can be realized by separation matrix:
In view of the specific features of aerodynamic force, for independent principal coordinate signal, the shellfish for considering aerodynamic characteristics can be used
This spectrum density method of leaf carries out intrinsic frequency and damping ratios under each principal coordinate of parameter identification acquisition.
Further, it is illustrated in combination with fig. 2 present implementation, step 3-3 carries out separation signal using curve-fitting method
Modal Parameter Identification, the specific steps are as follows:
S3-3-1: the power spectral density of separation signal q (t) is calculated；
S3-3-2: the power spectral density S of the separation signal q (t) containing undetermined parameter is calculatedq(fk),
S3-3-3: load response Y (t) the power spectral density S for considering influence of noise is calculatedY,N(fk) expectation E [SY,N(fk)|
θ], E [SY,N(fk) | θ]=E [Sq,N(fk)|θ]+Sη；
S3-3-4: S is calculatedY,N(fk) probability density function p (SY,N(fk)|θ)；
S3-3-5: joint probability density distribution function is calculated
S3-3-6: the posterior probability density function of modal parameter is calculated
S3-3-7: the minimum value of J (θ) is solved, the uncertainty estimation of undetermined parameter and relevant parameter is obtained.
According to being described in detail the step of S3-3-1 to S3-3-7, single-degree-of-freedom linear vibrating system, standardization are considered
Kinetics equation are as follows:
Q in formulam(t) the model top displacement response to be converted by measuring bottom displacement；mmFor the modal mass of MBS；
P (t) is the random load excitation acted in structure.
It is divided according to the property of power, load can be motivated and be divided into white-noise excitation (or approximate white-noise excitation) and coloured make an uproar
Acoustically-driven.The power spectral density of white-noise excitation is constant, largely based on the parameter identification method of white-noise excitation to white noise
The parameter of excitation identifies also accuracy with higher.Coloured noise is motivated, according to the phase of itself and the intrinsic frequency of system
Position is divided, coloured noise and excellent frequency of the excellent frequency far from intrinsic frequency can be divided into and be located at the coloured of interval of resonance
Noise.The former is in the skew lines downward trend under log-log coordinate, and there are extreme values in section by the latter.
Based on features above and the research achievement of related journals and data is summarized, the broad sense summarized under different wind speed is pneumatic
The feature of the power spectral density of load, expression formula are as follows:
ε, β, γ and λ indicate four undetermined parameters of aerodynamic force in formula.When β, γ and λ are 0, above is white noise
Excitation.When γ and λ are 0, it is S that formula (12), which is degenerated,p(f)=ε fβ, it is in a skew lines under log-log coordinate.Fig. 3 is provided
It is based on the aerodynamic force matched curve of formula (12).As seen from the figure, under different directions matched curve and measuring signal power spectrum
It is higher to spend the goodness of fit, shows to assume that formula all has preferable fitting effect to down wind and across-wind loads.It also sends out simultaneously
The fit range of existing down wind aerodynamic force is wider, and beam wind to fit range it is relatively narrow, this is because the basad load of beam wind
There are biggish uncertainties for power spectral value of the power spectral density in the frequency band after excellent frequency, thus suggest in not shadow
Ring frequency identification in the case where, can by beam wind to fit range suitably reduce.
Assuming that the load response measured are as follows:
Y (t)=qj(t)+η(t) (13)
η (t) is the prediction between system real response caused by measuring noise and model error etc. and systematic survey response
Error, and it is assumed to the Band-Limited White Noise for meeting normal distribution of zero-mean, variance and power spectral density are distributed as
And Sη, meet following relationship:
Sampling time interval when Δ t is measurement.
Y (t) power spectral density SY,N(fk) expectation are as follows:
E[SY,N(fk) | θ]=E [Sq,N(fk)|θ]+Sη (15)
In formula, fk=k Δ f, k=0,1 ..., int (N/2), int expression take the integer part of real number,T is to adopt
The sample time.θ is the modal parameter for needing to identify, including natural frequency of structures f0,j, dampingratioζj, ε, β, γ and λ in undetermined parameter
And prediction error-spectral density Sη。
When N is sufficiently large, can prove that
According to random vibration theory, the response of available equation (11) are as follows:
For stationary process, in specific frequency separation section, SY,N(fk) probability distribution can be approximated to be Chi-square
Distribution, probability density function indicate are as follows:
Work as k1≠k2When,WithIt is irrelevant in same frequency separation section, thus its joint probability is close
Degree distribution function may be expressed as:
For a reasonable approximate frequency segment, which is usually taken near structural response spectrum peak
One section of region.
According to Bayes' theorem, the posterior probability density function of modal parameter:
D is an iotazation constant, and p (θ) is priori probability density function, and the two is generally viewed as constant in calculating.
The optimal solution (Most Probable Value, MPV) of modal parameter can be by solving following functional minimum value
To determine:
Further, step 3-4 emphasizes the parameter obtained according to identification, is modified to separation signal.
The separation matrix obtained according to above methodIt, can be with and by each modal parameter for identifying of decoupling source signal
Obtain the power spectral density matrix of revised model substrate aerodynamic force under modal coordinate are as follows:
In formula, h (f) is the frequency response function h of each principal coordinatei(f) the multiple diagonal matrix constituted,The Hermite transposition of subscript H representing matrix.
Fig. 4 gives the correction effect figure after separation, it can be seen that the correction effect to separation signal is more satisfactory.
Further, step 3-5 points out to obtain revised pneumatic load by separation signal backstepping.According to modal coordinate
Transformational relation between physical coordinates, obtains:
The calibration effect in the case of modal coupling is set forth in Fig. 5, and as can be seen from the figure above method can carry out
Good power calibration.
So far, the power calibration of the part BMS is all introduced and is finished,It is to further calculate super high-rise building
The important evidence of wind-excited responese.
Further, signal exports after step 4 will calibrate, and obtains acquisition signal.
Influence comparison diagram whether Fig. 6 gives amendment to equivalent foundation load, as seen from the figure, signal correction is to substrate lotus
The average value of load does not influence, this is because signal correction is the power augmentation effect progress for structure, with static(al) part
It is unrelated.Simultaneously it has also been found that the absolute value of revised structure wind-excited responese is less than uncorrected result.Wherein with 30 ° of Mx,
150 ° nearby and before and after the amendment near 30 °, 150 ° and 270 ° of My result difference is maximum.For translational direction,
The difference of torsional direction amendment front and back will be significantly less than translational direction.
Further, step 5: by acquisition signal reduced scale transformation, the foundation load of prototype is obtained, detailed process is as follows:
Signal after calibration is the model signals that test measures, and needs to convert model signals to architecture prototyping signal.Tool
Steps are as follows for body:
S1: the wind speed calculation of wind speed scaling factor η of the reference altitude measured first by local fundamental wind pressure and testv, into
And obtain wind pressure scaling factor ηw=ηv 2；
S2: by geometry scaling factor ηLWith wind speed scaling factor ηvCalculate time scaling factor ηt=ηL/ηv, and then obtain frequency reduced scale
Compare ηf=1/ ηt；
S3: by wind pressure scaling factor ηwWith geometry scaling factor ηLObtain substrate moment of flexure or torque scaling factorAnd base
Bottom shears scaling factor
S4: revised model signals can be converted to the substrate load x ' (t) of practical structures by the above scaling factor and adopted
Sample frequency.
Further, step 6 is emphasized to acquire mode distribution coefficient matrix by modal analysis result, and detailed process is as follows:
Mode distribution coefficient Matrix C may be expressed as:
C obtains vibration shape φ by model analysis and acquires, it then follows all directions component specific gravity shared in generalized mass is constant
Principle.
K respectively indicates x, y and torsional direction in formula.
Further, step 7: in conjunction with mode distribution coefficient matrix, substrate aerodynamic force is obtained, the specific steps of which are as follows:
S1: the structural eigenvector Φ for considering modal coupling is calculated by mode distribution coefficient Matrix C；
S2: substrate aerodynamic force is calculated by structural eigenvector Φ and the pneumatic force signal x ' (t) of revised prototype.
In architecture prototyping system, differential equation of motion of the super high-rise building under fluctuating wind effect are as follows:
M, D and K are respectively quality, damping and the stiffness matrix of architecture prototyping system in formula；fAIt (t) is revised pneumatic
Power；It is respectively acceleration, speed and the dynamic respond of structure with δ (t).
Using moda1 decomposition method, displacement can be indicated are as follows:
δ (t)=Φ q (t) (27)
Φ and q (t) is respectively structural eigenvector matrix and generalized coordinates in formula.Preceding 3 rank mode is only considered for HFFB method
Influence, and assume that the vibration shape of each rank mode is distributed along highly linear, Φ matrix can be write as mode distribution coefficient Matrix C
Kronecker (Kronecker) product, is denoted as:
Z=[z in formula1 z2 … zn]T, indicate each story height, altogether n-layer, H is building height, Cx,j、Cy,jAnd Cθ,jPoint
Not Wei x, y and torsional component jth rank mode distribution coefficient,
By the vibration shape orthogonality and assume that damping matrix can be decoupled, then can be obtained through mode decomposition and transported under modal coordinate
The dynamic differential equation are as follows:
In formulaAnd Kp=MpΛ points
Not Wei modal mass, modal damping and modal stiffness matrix, whereinωjAnd ζjJth respectively
Modal mass, intrinsic frequency and the damping ratio of rank mode.fA(z, t) is the pneumatic load of each floor for including 3 directions, and equation is right
End is broad sense aerodynamic force, is denoted as:
M in formulaA,x(t) and MA,y(t) respectively around the pneumatic moment of flexure of substrate x and y-axis, MA,T(t) for around the broad sense gas of z-axis
Dynamic torque, are as follows:
It cannot directly be obtained with the total aerodynamic moment of substrate of measurement, the sum of each floor aerodynamic moment of the latter:
MA,z(t)=∑ fA,T(t) (32)
It, can be using the following modification method relatively guarded based on the statistical result of simultaneous multi-pressure measurement test:
MA,T(t)=0.7MA,z(t) (33)
Note:
Then above generalized force can be write as:
F (t)=BT[MA,y(t) MA,x(t) MA,z(t)]T (35)
Have by the definition of upper section:
F (t)=BTx′(t) (36)
Further, step 8 obtains substrate moment of flexure and torque responsive, and its step are as follows:
S1: Fourier transformation is carried out to basic aerodynamic force, obtains frequency-region signal F (ω, T)；
S2: the modal response q (ω, T) in frequency domain is solved according to F (ω, T)；
S3: the frequency domain response δ (ω, T) of practical structures is solved according to q (ω, T)；
S4: the power spectral density matrix and covariance matrix of q (t) are calculated；
S5: the power spectral density matrix and covariance matrix of δ (t) are calculated；
S6: the covariance matrix of acceleration under mode and physical coordinates is calculated.
And Fourier transformation is carried out to finite length sample by formula, then have:
F (ω, T)=BTX′(ω,T) (37)
The Fourier transformation of structural modal response can be obtained are as follows:
In formulaFor the frequency response function square of structural modal coordinate
Battle array, in which:
ζ in formulajAnd ωjFor structure jth rank damping ratios and inherent circular frequency.Respective physical coordinate can be obtained by formula (27)
Under frequency domain response are as follows:
δ (ω, T)=Φ q (ω, T) (40)
In the sufficiently long situation of sample, the power spectral density matrix for obtaining q (t) may be calculated as:
Then its corresponding covariance matrix are as follows:
The power spectral density matrix of q (t) can be indicated if formula (38) are substituted into (41) are as follows:
It obtains the power spectral density responded under physical coordinates in turn and covariance matrix is respectively as follows:
Cδ=Φ CqΦT (45)
The power spectral density of its corresponding acceleration accordingly can be obtained by the power spectral density that modal coordinate responds:
The covariance matrix of mode and physical coordinates acceleration is respectively as follows:
Further, step 9 obtains in equivalent static wind load, after obtaining non trivial solution, the bullet of available system
Property restoring force fE(z, t) are as follows:
Define the influence matrix of substrate internal force (overturning moment, torque and shearing):
U is the unit column matrix with the same length of z in formula.The then equivalent substrate internal force x of structureE(t) it can be write as:
xE(t)=ΨTMΦΛq(t) (51)
Enable the equivalent matrix E=Ψ of loadTM Φ Λ, then above formula can simplify are as follows:
xE(t)=Eq (t) (52)
The covariance matrix of substrate internal force can be obtained by result above are as follows:
It can thus be concluded that the extreme value load of each component are as follows:
In formulaFor the average value of each component, can be directly acquired by test；G is peak factor；For force component in substrate
Mean square deviation,
Influence comparison diagram whether Fig. 7 gives modal coupling to equivalent foundation load.As seen from the figure, modal coupling equity
The average value of effect foundation load does not influence.Meanwhile the equivalent basis under certain angles (near such as 25 °) under non-coupling condition
Load Mx is greater than the value under coupling condition, and under other angle (near such as 270 °), the equivalent foundation load of coupling is big
In non-coupling value.That is, coupling is with the equivalent foundation load under non-coupling condition, there is no absolutely big or absolutely small
Situation, thus the value under its coupling condition can not be gone out by foundation load simple inference equivalent under non-coupling condition.
The above embodiment is a preferred embodiment of the present invention, but embodiments of the present invention are not by above-described embodiment
Limitation, other any changes, modifications, substitutions, combinations, simplifications made without departing from the spirit and principles of the present invention,
It should be equivalent substitute mode, be included within the scope of the present invention.
Claims (8)
1. considering the wind shake implementation method of double coupled systems of radio frequency plasma CVD test, which is characterized in that including following step
It is rapid:
S1: voltage signal is obtained by wind tunnel test measurement；
S2: initial substrate load signal is obtained through static calibration；
S3: being calibrated by power, obtains final substrate load signal；The power calibration is primarily based on the second order of complex modal theory
Blind discrimination technology realizes the decoupling to coupling measurement signal, then uses Bayes's spectrum density method pair based on full aerodynamic simulation
Separate signal and carry out reliable parameter identification, obtain separation/hybrid matrix of balance model system test signal, intrinsic frequency and
Damping ratio realizes the amendment to the pneumatic force signal of distortion measurement；
S4: signal after calibration is exported, and obtains acquisition signal；
S5: by acquisition signal reduced scale transformation, the foundation load of prototype is obtained；
S6: mode distribution coefficient matrix is acquired by modal analysis result, the mode distribution coefficient matrix is obtained by model analysis
The vibration shape acquires, it then follows the constant principle of all directions component specific gravity shared in generalized mass；The matrix mode distribution coefficient
Matrix is expressed as:
Wherein, θ indicates torsional direction；X and y indicates two orthogonal translational directions, Cx,1、Cy,1And Cθ,1Respectively indicate
X, y of first-order modal and the mode distribution coefficient of torsional direction, first subscript indicate direction, and second subscript indicates mode rank
Number；
S7: in conjunction with mode distribution coefficient matrix, the substrate aerodynamic force of architecture prototyping system is obtained, comprising:
S7-1: the structural eigenvector Φ for considering modal coupling is calculated by mode distribution coefficient Matrix C；
S7-2: substrate aerodynamic force is calculated by structural eigenvector Φ and the pneumatic force signal x ' (t) of revised prototype；
S8: substrate moment of flexure and torque responsive are obtained, comprising:
S8-1: Fourier transformation is carried out to basic aerodynamic force, obtains frequency-region signal F (ω, T)；
S8-2: the modal response q (ω, T) in frequency domain is solved according to frequency-region signal F (ω, T)；
S8-3: the frequency domain response δ (ω, T) of practical structures is solved according to modal response q (ω, T)；
S8-4: the power spectral density matrix and covariance matrix of generalized coordinates q (t) are calculated；
S8-5: the power spectral density matrix and covariance matrix of the dynamic respond δ (t) of architecture prototyping are calculated；
S8-6: the covariance matrix of acceleration under mode and physical coordinates is calculated；
S9: equivalent static wind load is obtained, comprising:
After obtaining non trivial solution, the elastic restoring force of system is obtained；
The influence matrix for defining substrate internal force, obtains the equivalent substrate internal force of structure, to obtain the covariance square of substrate internal force
Battle array；
Thus the extreme value load of each component is obtained.
2. the wind shake implementation method of the double coupled systems according to claim 1 for considering radio frequency plasma CVD test,
It is characterized in that, the process for calibrating to obtain final substrate load signal by power of step S3 includes:
S3-1: plural numberization processing is carried out to measuring signal x (t), obtains complex signal
S3-2: to complex signalIt carries out albefaction and obtains signal after albefaction
S3-3: seeking orthogonal matrix V, so thatAnd then the complex signal after being separated
S3-4: under modal coordinate, intrinsic frequency is carried out to separation signal and damping ratios identify；
S3-5: the parameter obtained according to identification is modified separation signal；
S3-6: by revised separation signal backstepping, revised pneumatic load is obtained；
Specifically, setting x (t)=[Mx(t) My(t) Mz(t)]TFor the HFFB pneumatic overturning moment in model basis observed and torsion
The vector signal that square is constituted, can be considered by one group of independent source signal qm(t) it mixes:
X (t)=Φmqm(t) (1)
Φ in formulamFor hybrid matrix, the vibration shape matrix being equivalent in dynamic structural analysis, it is assumed that its sequency spectrum is reversible；qm(t) then
For the principal coordinate function of balance model system；Following method source signal q isolated to progress to x (t) can be usedm(t):
Plural numberization processing is first carried out to x (t) using Hilbert transform method, on this basis to complex signalCovariance square
Battle array:
Eigenvalues Decomposition is carried out, obtains corresponding eigenvectors matrix E and diagonal matrix characteristic value D, and thus obtain so-called white
Change matrix W are as follows:
W=ED-1/2 (3)
By whitening matrix W to complex signalPrincipal component decomposition is carried out, signal after albefaction is obtained:
MeetFor unit battle array；It is similar with formula (1), complex signalIt can be expressed as
Above formula substitution formula (4) is obtained:
Wherein,
Its corresponding time delay correlation function matrix are as follows:
Wherein: τ is time delay,For the complex signal after separationTime delay correlation function matrix, t is the time；
Due toIn each element it is mutually indepedent, and set its variance as 1；And signal after albefactionThe orthogonal normalizing of middle each element,
Therefore V must be orthogonal normalizing battle array；About the solution of orthogonal matrix V, JAD method can be used；After obtaining orthogonal matrix V, it can be able to
Lower hybrid matrix and separation matrix:
The source signal of the isolated decoupling to signal can be realized by separation matrix:
In view of the specific features of aerodynamic force, for independent principal coordinate signal, the Bayes for considering aerodynamic characteristics can be used
Spectrum density method carries out intrinsic frequency and damping ratios under each principal coordinate of parameter identification acquisition；
According to obtained separation matrixAnd the modal parameter identified by each decoupling source signal, available modal coordinate
Under revised model substrate aerodynamic force power spectral density matrix are as follows:
In formula,For complex signalPower spectral density matrix, h (f) be each principal coordinate frequency response function hi(f) structure
At multiple diagonal matrix,f0,jAnd ζjThe respectively natural frequency of vibration and resistance of jth rank mode
Buddhist nun's ratio, j are rank number of mode；I is principal coordinate order, i=j；The Hermite transposition of subscript H representing matrix；
By separation signal backstepping, revised pneumatic load is obtained, according to the transformational relation between modal coordinate and physical coordinates,
It obtains:
Wherein: Φ is structural eigenvector matrix.
3. the wind shake implementation method of the double coupled systems according to claim 2 for considering radio frequency plasma CVD test,
It is characterized in that, step S3-3 carries out Modal Parameter Identification to separation signal using curve-fitting method, includes the following steps:
S3-3-1: the power spectral density of separation signal q (t) is calculated；
S3-3-2: the power spectral density S of the separation signal q (t) containing undetermined parameter is calculatedq(fk),fk=k Δ f, k=0,1 ..., int (N/2), int expression take real number
Integer part,T is the sampling time；
S3-3-3: load response Y (t) the power spectral density S for considering influence of noise is calculatedY,N(fk) expectation E [SY,N(fk) | θ], E
[SY,N(fk) | θ]=E [Sq,N(fk)|θ]+Sη；Sq,N(fk) be system real response power spectral density, θ be the mould that identifies of needs
State parameter, SηTo predict error-spectral density；
S3-3-4: S is calculatedY,N(fk) probability density function p (SY,N(fk)|θ)；
S3-3-5: joint probability density distribution function is calculated It is one
Reasonable approximate frequency segment, the segment usually take one section of region near structural response spectrum peak；
S3-3-6: the posterior probability density function of modal parameter is calculatedP (θ) is prior probability
Density function；
S3-3-7: the minimum value of J (θ) is solved, the uncertainty estimation of undetermined parameter and relevant parameter is obtained；
Specifically, considering single-degree-of-freedom linear vibrating system, standardized kinetics equation are as follows:
In formula: qm(t) the model top displacement response to be converted by measuring bottom displacement；mmFor the modal mass of MBS；p
(t) it is motivated to act on the random load in structure；For acceleration responsive at the top of model,For model top speed
Response, ωjFor the inherent circular frequency of jth rank mode；ζjFor the damping ratio of jth rank mode；
The feature of the power spectral density of the pneumatic load of broad sense under different wind speed, expression formula are as follows:
ε, β, γ and λ indicate four undetermined parameters of aerodynamic force in formula；When β, γ and λ are 0, above is that white noise swashs
It encourages, when γ and λ is 0, it is S that formula (13), which is degenerated,p(f)=ε fβ, it is in a skew lines under log-log coordinate；
Assuming that the load response measured are as follows:
Y (t)=qj(t)+η(t) (14)
Wherein: qjIt (t) is system real response, η (t) is system real response and system caused by measurement noise and model error
Measurement response between prediction error, and be assumed to zero-mean the Band-Limited White Noise for meeting normal distribution, variance and
Power spectral density is distributed asAnd Sη, meet following relationship:
Sampling time interval when Δ t is measurement；
Y (t) power spectral density SY,N(fk) expectation are as follows:
E[SY,N(fk) | θ]=E [Sq,N(fk)|θ]+Sη (16)
In formula, fk=k Δ f, k=0,1 ..., int (N/2), int expression take the integer part of real number,When T is sampling
Between；θ is the modal parameter for needing to identify, including natural frequency of structures f0,j, dampingratioζj, in undetermined parameter ε, β, γ and λ and
Predict error-spectral density Sη；
When N is sufficiently large, can prove that
According to random vibration theory, the response of available equation (11) are as follows:
For stationary process, in specific frequency separation section, SY,N(fk) probability distribution can be approximated to be Chi-square distribution,
Its probability density function indicates are as follows:
k1And k2For respective frequencies sequence fkThe different position of middle any two, and k1≤k2, work as k1≠k2When,WithIt is irrelevant in same frequency separation section, thus its joint probability density distribution function may be expressed as:
For a reasonable approximate frequency segment, which usually takes one near structural response spectrum peak
Section region；
According to Bayes' theorem, the posterior probability density function of modal parameter:
D is an iotazation constant, and p (θ) is priori probability density function, and the two is considered as constant in calculating；
The optimal solution of modal parameter can be determined by solving following functional minimum value:
4. the wind shake implementation method of the double coupled systems according to claim 3 for considering radio frequency plasma CVD test,
It is characterized in that, step S5, by acquisition signal reduced scale transformation, obtains the foundation load of prototype, comprising the following steps:
S5-1: the wind speed calculation of wind speed scaling factor η of the reference altitude measured first by local fundamental wind pressure and testv, and then
To wind pressure scaling factor ηw=ηv 2；
S5-2: by geometry scaling factor ηLWith wind speed scaling factor ηvCalculate time scaling factor ηt=ηL/ηv, and then obtain frequency scaling factor
ηf=1/ ηt；
S5-3: by wind pressure scaling factor ηwWith geometry scaling factor ηLObtain substrate moment of flexure or torque scaling factorIt is cut with substrate
Power scaling factor
S5-4: revised model signals can be converted to by the above scaling factor substrate load and sample frequency of practical structures.
5. the wind shake implementation method of the double coupled systems according to claim 4 for considering radio frequency plasma CVD test,
It is characterized in that, step S6, mode distribution coefficient matrix is acquired by modal analysis result, comprising the following steps:
Mode distribution coefficient Matrix C may be expressed as:
Wherein, θ is torsional direction；
C obtains vibration shape φ by model analysis and acquires, it then follows the constant principle of all directions component specific gravity shared in generalized mass；
In formula: k respectively indicates x, y and torsional direction, i.e. k is variable, and what k was indicated is direction, can be x, appointing in y or torsion
Meaning one；φk,jFor the vibration shape of jth rank mode under the direction k, m is the architecture quality matrix extracted in model analysis.
6. the wind shake implementation method of the double coupled systems according to claim 5 for considering radio frequency plasma CVD test,
It is characterized in that, step S7, in conjunction with mode distribution coefficient matrix, obtains substrate aerodynamic force, specifically:
In architecture prototyping system, differential equation of motion of the super high-rise building under fluctuating wind effect are as follows:
M, D and K are respectively quality, damping and the stiffness matrix of architecture prototyping system in formula；fAIt (t) is revised aerodynamic force；It is respectively acceleration, speed and the dynamic respond of structure with δ (t)；
Using moda1 decomposition method, displacement can be indicated are as follows:
δ (t)=Φ q (t) (26)
Φ and q (t) is respectively structural eigenvector matrix and generalized coordinates in formula；The shadow of preceding 3 rank mode is only considered for HFFB method
It rings, and assumes that the vibration shape of each rank mode is distributed along highly linear, Φ matrix can be write as the Crow of mode distribution coefficient Matrix C
Interior gram of product, is denoted as:
Z=[z in formula1 z2 … zn]T, indicate each story height, altogether n-layer, H is building height, Cx,j、Cy,jAnd Cθ,jRespectively x,
The jth rank modal participation factors of y and torsional component；
By the vibration shape orthogonality and assume that damping matrix can be decoupled, then can be obtained through mode decomposition moved under modal coordinate it is micro-
Divide equation are as follows:
In formula:For modal acceleration,For modal velocity, q (t) is modal displacement, And Kp=MpΛ is respectively modal mass, modal damping and modal stiffness matrix,
Wherein ωjAnd ζjModal mass, intrinsic frequency and the damping ratio of jth rank mode respectively；fA
(z, t) is the pneumatic load of each floor for including 3 directions, and equation right end is broad sense aerodynamic force, is denoted as:
M in formulaA,x(t) and MA,y(t) respectively around the pneumatic moment of flexure of substrate x and y-axis, MA,T(t) it is pneumatically turned round for the broad sense around z-axis
Square, are as follows:
It cannot directly be obtained with the total aerodynamic moment of substrate of measurement, the sum of each floor aerodynamic moment of the latter:
MA,z(t)=∑ fA,T(t) (31)
It, can be using the following modification method relatively guarded based on the statistical result of simultaneous multi-pressure measurement test:
MA,T(t)=0.7MA,z(t) (32)
Note:
Then above generalized force can be write as:
F (t)=BT[MA,y(t) MA,x(t) MA,z(t)]T (34)
If x ' (t)=[MA,y(t) MA,x(t) MA,z(t)]T, then:
F (t)=BTx′(t)。 (35)
7. the wind shake implementation method of the double coupled systems according to claim 6 for considering radio frequency plasma CVD test,
It is characterized in that, step S8 obtains substrate moment of flexure and torque responsive, specifically:
Fourier transformation is carried out to finite length sample by formula, then is had:
F (ω, T)=BTX′(ω,T) (36)
The Fourier transformation of structural modal response can be obtained are as follows:
In formula:For modal stiffness matrix KpIt is inverse,For structural modal
The frequency response function matrix of coordinate, in which:
ζ in formulajAnd ωjFor the jth rank damping ratios and inherent circular frequency of structure；It can be obtained under respective physical coordinate by formula (26)
Frequency domain response are as follows:
δ (ω, T)=Φ q (ω, T) (39)
In the sufficiently long situation of sample, the power spectral density matrix for obtaining q (t) may be calculated as:
Then its corresponding covariance matrix are as follows:
The power spectral density matrix of q (t) can be indicated if formula (37) are substituted into (40) are as follows:
Wherein Sx′(ω) is the power spectral density matrix of x ' (t), and then obtains the power spectral density responded under physical coordinates and association
Variance matrix is respectively as follows:
Cδ=Φ CqΦT (44)
The power spectral density of its corresponding acceleration accordingly can be obtained by the power spectral density that modal coordinate responds:
The covariance matrix of mode and physical coordinates acceleration is respectively as follows:
8. the wind shake implementation method of the double coupled systems according to claim 7 for considering radio frequency plasma CVD test,
It being characterized in that, step S9 is obtained in equivalent static wind load, after obtaining non trivial solution, the elastic restoring force of available system
fE(z, t) are as follows:
Wherein: K is the stiffness matrix of architecture prototyping system, and Λ is diagonal inherent circular frequency matrix,
Q (t) is generalized coordinates, and M is the mass matrix of architecture prototyping system；
Define the influence matrix of substrate internal force:
U is the unit column matrix with the same length of z in formula；The then equivalent substrate internal force x of structureE(t) it can be write as:
xE(t)=ΨTMΦΛq(t) (50)
Enable the equivalent matrix E=Ψ of loadTM Φ Λ, then above formula can simplify are as follows:
xE(t)=Eq (t) (51)
The covariance matrix of substrate internal force can be obtained by result above are as follows:
It can thus be concluded that the extreme value load of each component are as follows:
In formulaFor the average value of each component, can be directly acquired by test；G is peak factor；For in substrate force component it is equal
Variance, For the covariance matrix of substrate internal force.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH05322693A (en) * | 1992-05-26 | 1993-12-07 | Mitsubishi Heavy Ind Ltd | Wind tunnel test device |
| JPH10115572A (en) * | 1996-10-11 | 1998-05-06 | Mitsubishi Electric Corp | Wind tunnel test apparatus |
| CN1851436A (en) * | 2006-05-31 | 2006-10-25 | 汕头大学 | Big-span roof and super high-rise building structure wind vibration response detecting and computing method |
| CN106709460A (en) * | 2016-12-28 | 2017-05-24 | 华南理工大学 | Dynamic calibration method for high-frequency force balance |
-
2018
- 2018-06-01 CN CN201810555482.5A patent/CN109060292B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH05322693A (en) * | 1992-05-26 | 1993-12-07 | Mitsubishi Heavy Ind Ltd | Wind tunnel test device |
| JPH10115572A (en) * | 1996-10-11 | 1998-05-06 | Mitsubishi Electric Corp | Wind tunnel test apparatus |
| CN1851436A (en) * | 2006-05-31 | 2006-10-25 | 汕头大学 | Big-span roof and super high-rise building structure wind vibration response detecting and computing method |
| CN106709460A (en) * | 2016-12-28 | 2017-05-24 | 华南理工大学 | Dynamic calibration method for high-frequency force balance |
Non-Patent Citations (3)
| Title |
|---|
| 改进贝叶斯谱密度法及其在超高层结构振动模态参数识别中的应用;潘浩然 等;《建筑结构学报》;20161231;第37卷(第12期);第27-32页 * |
| 格构式塔架结构的等效静力风荷载与风振响应分析;张乐乐;《万方数据》;20150817;第I、4-71页 * |
| 风致复杂结构随机振动分析的一种快速算法——谐波激励法;谢壮宁;《应用力学学报》;20070630;第24卷(第2期);第263-267页 * |
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